Abstract
Knowledge of bounds and equalities for the exact density-functional exchange-correlation potential δ[n]/δn(r) is necessary for its accurate approximation. With this in mind, it is shown, for λ→0, that Frn(r)δ[]/ δn(r)≥2[] and Fn(r’)‖r-r’r’ +δ[]/δn(r)≥0, where (x,y,z)=n(λx,λy,λz). The local-density approximation satisfies the former inequality but violates the latter one. Moreover, with respect to the Fermi level, it is shown that the exact correlation potential δ[n]/δn(r) satisfies [n]-[n-Δ]≤Fδ[n]/ δn(r)Δ(r)r, where Δ is the density of the highest-occupied Kohn-Sham orbital of n. The corresponding inequality for the exact exchange potential δ[n]/δn(r) is in the opposite direction: [n]-[n-Δ]≥Fδ[n]/ δn(r)Δ(r)r. It is a difficult challenge for an approximate exchange-correlation functional to simultaneously satisfy both inequalities. For instance, the local-density approximation does not.
- Received 6 June 1994
DOI:https://doi.org/10.1103/PhysRevA.51.2851
©1995 American Physical Society